The complex microstructures of the cast stainless steel found in nuclear reactors makes their ultrasonic nondestructive evaluation particularly difficult. Of concern in certain cast steels are the highly aligned grain structures that develop, creating significant elastic anisotropy and variation of wave speeds with direction. The dependence of wave speed on propagation direction, in turn, leads to such phenomena as beam skewing and excess beam divergence. Furthermore, when components of these materials are integrated into a structure by welding, additional inhomogeneities are introduced. In various components, there may be one or more layers with different anisotropy and grain morphology, separated by discrete interfaces, or there may be regions in which the properties change continuously. Examples of the latter are found within the weldment itself, where the direction of anisotropy continuously changes in response to the direction of heat flow during solidification. Understanding and developing appropriate theories for beam propagation through such inhomogeneous, anisotropic cast stainless steel components has been the subject of recent interest for researchers; codes have been developed using finite difference, and finite element and ray tracing methods. The finite difference (1) and finite element (2) techniques produce exact solutions and can treat very complex geometries; however, they require a long computation time. On the other hand, ray tracing (3) is relatively fast but does not treat beam spreading properly.